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26 January 2016Study on choice of excellent college coaches based on the weighted sum model (Withdrawal Notice)

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Publisher’s Note: This paper, originally published on 26 January 2016, was withdrawn. If you have any questions please contact SPIE Digital Library Customer Service for assistance.

1.

INTRODUCTION

The coach’s professional quality, charisma, and ability of control on the court have a great impact on the team. A good coach will be able to train a very competitive team. At present the main method of evaluating the college coaches is a comprehensive evaluation method, such as the Delphi method [1], entropy value method [2], principal component analysis (PCA) [3] and analytic hierarchy process (AHP) [4-5]. Among them, the most commonly used method are the PCA and AHP. The PCA is a kind of objective method, its main advantage lies in that it can avoid the redundancy of information based on the correlation coefficient matrix, and its disadvantage is that when the correlation of important information and other information is weaker, the important information may be omitted. AHP method is a kind of subjective method. The judgment matrix need to be subjectively weighted, and the results of researchers at different times may have a bigger difference. In the methods above, the establishment of the index system is the foundation of index system, which has a strong operability. But in different composition benchmark, the index system is different [6-8]. Here, the weighted sum model will be built to evaluate the college coaches in the sports of basketball, football and softball comprehensively.

2.

WEIGHTED SUM MODEL

2.1

Determination of the major indexes of coaches and their weights

In general, the team’s performance and work experience of coaches are the objective reflections of the comprehensive ability of the coaches. Therefore, according to the available data, the W-L% (Win-Loss Percentage), NC (Number of NCAA tournament championships won), FF (Number of NCAA Final Four appearance), NCAA (Number of NCAA tournament appearance), CTRN (Number of conference tournament championships won), CRGE (Number of regular season conference championships won), and Yrs (Teaching years) are selected as the major indexes of coaches in the sport of basketball; W-L% (Win-Loss Percentage), W-L% of Bowl (Win-Loss Percentage of Bowl), Bowl, G (Total coaching session) and Yrs (Teaching years) are selected as the major indexes of coaches in the sport of football; the W-L% (Win-Loss Percentage), G (Total coaching session)and Yrs (Teaching years) are selected as the major indexes of coaches in the sport of softball.

After determination of the major indexes of coaches in each of 3 different sports (basketball, football and softball), their weights wp can be determined. In each sport, the major indexes have different levels of importance. For example, in the sport of basketball, it has the following orders

So the weights of the major indexes of coaches in each of 3 different sports are determined by AHP. The rule is defined as follows:

If Level (A) > Level (B), then the result counts as 1; If Level (A) < Level (B), then the result counts as 0; And if Level (A) = Level (B), then the result counts as 0.5.

Therefore, the weights of the major indexes of coaches in each of 3 different sports can be determined and showed in

It can be seen that the weight (W-L%) is maximum, and weight (Yrs) is minimum, which indicates that W-L% (Win-Loss Percentage) is the most important index of coaches in each of 3 different sports.

Table 1.

Weights of the each major index of coaches in the sport of basketball.

Indexes

W-L%

NC

FF

NCAA

CTRN

CREG

Yrs

Sum

wp

W-L%

0.5

1

1

1

1

1

1

6.5

0.27

NC

0

0.5

1

1

1

1

1

5.5

0.23

FF

0

0

0.5

1

1

1

1

4.5

0.18

NCAA

0

0

0

0.5

1

1

1

3.5

0.14

CTRN

0

0

0

0

0.5

1

1

2.5

0.10

CREG

0

0

0

0

0

0.5

1

1.5

0.06

Yrs

0

0

0

0

0

0

0.5

0.5

0.02

Table 2.

Weights of the each major index of coaches in the sport of football.

Indexes

W-L% of Bowl

W-L%

Bowl

G

Yrs

Sum

wp

W-L% of Bowl

0.5

1

1

1

1

4.5

0.36

W-L%

0

0.5

1

1

1

3.5

0.28

Bowl

0

0

0.5

1

1

2.5

0.2

G

0

0

0

0.5

1

1.5

0.12

Yrs

0

0

0

0

0.5

0.5

0.04

Table 3.

Weights of the each major index of coaches in the sport of softball.

Indexes

W-L%

G

Yrs

Sum

wp

W-L%

0.5

1

1

2.5

0.56

G

0

0.5

1

1.5

0.33

Yrs

0

0

0.5

0.5

0.11

2.2

Normalization of data of the major indexes

In order to be convenient for data processing in programming, it should be normalized the data of the major indexes. In some type of sport, let S be the number of coaches, i = 1,2,…,S ; N be the number of major indexes of coaches, p = 1,2,…,N . S dimensional vector Gp is defined as follows

Each element in Gp is normalized by the Equation

Where Gpmax is the maximum element in vector Gp , and Gpmin is the minimum element in vector GpS dimensional vector Rp is defined as follows

Now the normalized vector Rp corresponding to vector Gp is obtained.

2.3

Establishment of the model to evaluate the comprehensive ability of the coaches

Based on 2.1 and 2.2, the scores Qi corresponding to the comprehensive ability of the coaches in each of 3 different sports are obtained by making the weighted summation as follows

Where wp is the weight of the p-th major index of coaches in each of 3 different sports.

From Equation (5), the 5 maximum Qi can be found out. So the top 5 coaches in each of 3 different sports based on the model can be determined.

2.4

Statistical results and analysis

According to the MATLAB programming, the scatter diagrams of the scores Qi corresponding to the comprehensive ability of the coaches in each of 3 different sports are obtained, as shown in Figures 1-3. And the top 5 coaches in each of 3 different sports based on the model are shown in Tables 4-6.

Figure 1.

Scatter diagram of the scores Qi corresponding to the comprehensive ability of the coaches in the sport of basketball.

Figure 2.

Scatter diagram of the scores Qi corresponding to the comprehensive ability of the coaches in the sport of football.

Figure 3.

Scatter diagram of the scores Qi corresponding to the comprehensive ability of the coaches in the sport of softball.

Table 4.

The top 5 coaches in the sport of basketball based on the model.

Coach

John Wooden

Mike Krzyzewski

Dean Smith

Adolph Rupp

Roy Williams

Last School

UCLA

Duke

North Carolina

Kentucky

North Carolina

Yrs

29

39

36

41

26

W-L%

0.804

0.764

0.776

0.822

0.793

NC

10

4

2

4

2

FF

12

11

11

6

7

NCAA

16

29

27

20

23

CTRN

0

10

13

13

6

CREG

16

12

17

28

15

Score

0.786

0.773

0.732

0.717

0.608

Table 5.

The top 5 coaches in the sport of football based on the model.

Coach

Joe Paterno

Bobby Bowden

Bear Bryant

Howard Jones

Fielding Yost

Last School

Penn State

Florida State

Alabama

Southern California

Michigan

Yrs

46

40

38

28

25

W-L% of Bowl

0.662

0.682

0.552

1

1

W-L%

0.749

0.74

0.78

0.732

0.833

Bowl

37

33

29

5

1

G

548

485

425

269

204

Score

0.807

0.769

0.697

0.667

0.660

Table 6.

The top 5 coaches in the sport of softball based on the model.

Coach

Margie Wright

Carol Hutchins

JoAnne Graf

Elaine Sortino

Mike Candrea

Last School

Fresno State

Michigan

Florida State

UMass

University of Arizona

Yrs

33

30

25

34

26

W-L%

0.729

0.747

0.735

0.699

0.806

G

2002

1777

1617

1699

1667

Score

0.615

0.637

0.638

0.639

0.656

From Figure 1 and Table 4, the share of excellent basketball coaches is much smaller, and the scores Qi of the best basketball coaches are much greater than the average 0.1917. The results of football and softball coaches are similar to those of basketball coaches. From Tables 4-6, it can be seen that the most of the top 5 college coaches in each of 3 different sports are well known to all, which verified the validity of the model to some extent.

3.

EFFECT OF THE TIME LINE HORIZON ON THE CHOICE OF THE BEST COLLEGE COACHES

According to the weighted sum model, W-L% (Win-Loss Percentage) is the most important index of coaches in each of 3 different sports. So based on the weighted sum model, the top 20 coaches were obtained in the sport of basketball. By using the available data of the top 20 coaches, the average of W-L% each year can be determined and shown in Figure 4. It can be seen that the fluctuations of the average of W-L% are high before 1939, and the fluctuations are low after 1939. So the time line horizon has greater effect on the choice of the best college coaches.

Figure 4.

The average of W-L% of all the basketball coaches each year.

The average of W-L% of all coaches each year in some sport WL is expressed as follows

Where ui is the W-L% each coach each year, and M is the number of coaches each year.

In addition, in order to give the change rule of the average of W-L% of all the basketball coaches, the curve fitting is made for the data in Figure 4, and the fitting result is shown in Fig. 5 (taking 1895 as initial year)). The fitting function is

From Figure 5, it can be seen that the average of W-L% decreased with the years, but kept stable at the end. It is mainly because with the increase of the number of matches, the matches become fairer, and becoming the best coach is more and more difficult.

Figure 5.

Fitting result of Figure 4.

4.

CONCLUSION

In this paper, the weighted sum model was built to evaluate the college coaches in the sports of basketball, football and softball comprehensively. Firstly, W-L%, CTRN, CRGE, NCAA, Yrs etc. are selected as the major indexes of coaches in different sports, and the weights of them were determined based on the weighted sum model. Then by making the weighted summation, the scores corresponding to the comprehensive ability of the coaches in each of 3 different sports were obtained, and the top 5 coaches in each of 3 different sports were found out. Because the time line horizon has greater effect on the choice of the best college coaches, so taking basketball as example, the college basketball coaches were divided into three types, the comprehensive ability of different types of coaches was evaluated, and the top 5 coaches in the sport of basketball were found out. The results showed that the top 5 college coaches in each of 3 different sports based on the model are well known to all, which verified the validity of the model to some extent.

ACKNOWLEDGMENT

This research is supported by the Scientific Research Foundation for the High-level Talents of Inner Mongolia Normal University (2014YJRC022), the National Science-technology Support Plan Program of China during the 12th Five-Year Plan Period (2013BAK05B01), the Natural Science Foundation of Inner Mongolia Autonomous Region (2013MS0107), and the National Natural Science Foundation of China (Grant No. 11562016 and 11362006).

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